Problem: If $m \angle AOC = 180^\circ$ and $m \angle BOC = 45^\circ$, what is $m \angle AOB$, in degrees? $45^\circ$ $O$ $A$ $C$ $B$
Explanation: From the diagram, we see that $\angle AOB$ and $\angle BOC$ are supplementary angles. Therefore, $m \angle AOB + m \angle BOC = 180^\circ$ Thus, $m \angle AOB = 180^\circ - m \angle BOC = 180^\circ - 45^\circ = 135^\circ$.